Rational Solutions of Parametric First-Order Algebraic Differential Equations
Sebastian Falkensteiner, Rafael Sendra
TL;DR
This paper introduces an algorithm to find rational solutions of first-order algebraic differential equations with parametric coefficients, analyzing their existence under parameter specialization.
Contribution
It provides a novel algorithm for solving parametric first-order ODEs and analyzes solution existence considering parameter specialization, advancing differential equation solution methods.
Findings
Algorithm successfully finds rational solutions for given equations.
Analysis of solution existence under parameter specialization.
Complete characterization modulo Hilbert's irreducibility problem.
Abstract
In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, complete modulo Hilbert's irreducibility problem, of the existence of rational solutions of the differential equation, with parametric coefficients, when the parameters are specialized.
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Taxonomy
TopicsNumerical methods for differential equations · Polynomial and algebraic computation · Nonlinear Waves and Solitons